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Atomic resolution electron microscopy
Dirk Van Dyck (Antwerp, Belgium)
Nato summer school Erice10 june 2011
Richard Feynman’s dream (1959)There’s plenty of room a the bottom:
an invitation to enter a new field of physics
It would be very easy to make an analysis of any complicated chemical substance; all one would have to do would be to look at it and see where the atoms are. The only trouble is that the electron microscope is one
hundred times too poor. I put this out as a challenge: Is there no way to make the electron microscope more
powerful?The sentence with the most information is: nature
consists of atoms
Characterization• structure• properties
TheoryModelling
DesignFabrication
understanding
Language: numbers (3D atomic positions (+/- 0.01 Angstrom))
Future of nanoscience
Bandgap engineering
Detection of individual particles Model based fitting Ultimate precision determined by the counting statistics Image is only an experimental dataset
Quantitative experiment
source object detectors
instrumental parameters
strong interaction
sub surface information
easy to detect
use of lenses (real space Fourier space)
electron beam brighter than synchrotron
less radiation damage than X-rays
larger scattering factor than X-rays
sensitive to charge of atoms.
Electrons are the best particles to Electrons are the best particles to investigate (aperiodic) nanostructuresinvestigate (aperiodic) nanostructures
7
Ultimate goal
•Quantitative model based fitting in 2D and 3D.
•Atoms are the ultimate alfabet.
•Extracting all information from HREM images
•Only limited by the statistical counting errors
8
Problem
•Model parameters (atom positions) scrambled in the experimental data
•Model based fitting : search for global fitness optimum in huge dimensional space
•Need to „resolve“ an approximate starting structure close to the global optimum: direct method
•Refinement : convergence and uniqueness guaranteed
04/19/23
Quantitative refinement
Resolving (direct method)
experiments atomic structure
Refining
EM: resolving atoms = new situation
Model based fitting (quantitative)
resolution precision
resolving refining
resolution precision
1 Å 0.01 Å
Å
ρ
σCR
resolution versus precision
Precision = resolution/ sqrt (dose)
Resolution = 1 Å
Dose = 10000 electrons
Precision =0.01Å
•Inverting the imaging: from image to exit wave
•Inverting the scattering:from exit wave to atomic structure
Step 2: refining (iterative)
•Model based fitting with experimental data
•Model for the imaging (image transfer theory)
•Model for the scattering (multislice, channelling)
Quantitative refinement in EM
Step 1: resolving (direct step)
Direct step
Inverting the imaging (Exit wave reconstruction)
Inverting the electron-object interaction (electron channelling)
Transfer in the microscopePrinciples of linear imaging
I(r) = O(r)*P(r) : convolution
O(r) = object function
P(r) = point spread function
Fourier space
I(g) = O(g).P(r) : multiplication
image deconvolution (deblurring)
Electron microscope: coherent imaging
image wave = object wave * point spread function
Electron interferenceMerli,Missiroli,Pozzi (Bologna1976)
Physics World (Poll 2002) : The most beautiful experiment in physics.
Point spread function and transfer function of the EM
point spread function(real space)
microscope’s transfer function(reciprocal space)
Measurement of the aberrations
Diffractogram
For weak objects
Amorphous: (Random):
White noise object
Measurement and (semi) automatic correction of the aberrations: Zemlin tableau
22
Intuitive image interpretation
• Phase transfer at optimum focus = pi/4
•Cfr phase plate in optics (Zernike)
•Phase contrast microscopy
•Weak phase object: phase proportional to projected potential
• Image contrast : projected potential
Image interpretation at optimum focus
Schematic representation of the unit cell of Ti2 Nb10O25
Comparison of experimental images (top row) (Iijima 1972) and computer-simulated images (bottom row) for Ti2 Nb10O25
N slices
Δz
NNn ppppqqqqr ]]]][[[[)( 22110012 Exit Wave functionExit Wave function
Ref: J. M. Cowley and A. F. Moodie, Acta Cryst. 10 (1957) 609
]),,(exp[ zzyxViq nn
]/)(exp[),( 22 zyxkiyxp
phase gratingphase grating
propagatorpropagator
Image simulation: the Multislice method
Best EM: resolution 0.5 Angstrom: resolving individual atoms
Ultimate resolution = atom
Transfer functions of TEM
0 1 20,0
0,5
1,0
1/A
1/A
1/A
1/A
detector
0 1 2-1
0
1electron microscope
0 1 20,0
0,5
1,0
thermal motion
0 1 20,0
0,5
1,0
Si atom
Image wave = object wave * impuls response
Deblurring (deconvolution) of the electron microscope
1) retrieve image phase: holography , focal series reconstruction2) deconvolute the (complex) point spread function3) reconstruct the (complex) exit wave of the object
OB*P
IIM = |IM|2
Inverting the imaging: from image to exit wave
From HREM images to exit wave
30
From exit wave to structureZone axis orientation
• Atoms superimpose along beam direction
• Electrons are captured in the columns
• Strong interaction: no plane waves
• Very sensitive to structure
• Atom column as a new basis
• Strong thermal diffuse scattering (absorption)
31
light atoms heavy atoms light atoms heavy atoms
zone axis orientation electron channelling
1s-state model (for one column)
)1)(1)(()0,(),( /1
iiEts eerrzr
reference wavebackground
Mass focus
positionwidth
DW-factorresidual aberrations
Diffraction pattern
Fourier transform of exit wave
Kinematic expression, with dynamical (thickness dependent) scattering factors of columns.
34
Channelling based crystallography
• Dynamical but local (symmetry is kept)
• Simple theory and insight
• Dynamical extinction
• Sensitive to light elements
• Exit wave more peaked than atoms
• Patterson (Dorset), direct methods (Kolb)
Phase of total exit wave 5 Al: Cu
Amplitude of
Phase of
Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)
5 Al + Cu
Phase of
38
Data mining the object wave
• Position of the atom columns (2D,3D)
• Weigth of the columns
• Single atom sensitivity
• Local Tilt
• Residual aberrations
•.....
1s-state model)
)1)(1)(()0,(),( /1
iiEts eerrzr
reference wavebackground
mass circle Defocus circle
positionwidth
DW-factorresidual aberrations
Argand Plot
exit wave - vacuum
vacuum
=
Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)
Argand plot of Au (100) (simulations)Single atom sensitivity
Graphene
Atomaire structuur in 3 dimensies
S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo.Nature 470 (2011) 374-377.
Number of Ag atoms from 2 projections
2D beelden van een zilver nanodeeltje in een aluminium matrix
[101] [100]
Discrete electron tomography
Atomaire structuur in 3 dimensies
S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo.Nature 470 (2011) 374-377.
46
Future
• Resolution gap imaging-diffraction is closing
• Exit wave same information as diffraction wave
• Quantitative precision only limited by dose
• Experiment design
• In situ experiments
• Femtosecond (4D) microscopy (Zewail)
47
• Resolution close to physical limits (atom)
• Resolution of imaging same as diffraction
• Applicable to non-periodic objects
• 3D atom positions with pm precision
• Precision only limited by dose
Conclusions
In-situ heating experimentsSublimation of PbSe
Marijn Van Huis (TU Delft)
Experiment design
Intuition is misleading
“Ideal” HREM: Cs = 0f = 0
“Ideal object”:phase object
we need a strategy
no image contrast
50 Å thick silicon [100] crystal at 300 kV
0.0 0.2 0.4 0.6 0.8 1.00.00
0.01
0.02
without correction for chromatic aberration with chromatic aberration corrector with monochromator
stan
dar
d d
evia
tio
n o
f p
osi
tio
n c
oo
rdin
ates
(Å
)
spherical aberration constant (mm)
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
0.4 without monochromator, without Cc-corrector
with monochromator with C
c-corrector
Lower bound on standard deviation of the positionC
s (mm)
Precision of a Si atom position as a function of CsAccelerating voltage = 50 keV
Resolution limits of HREM (Courtesy C Kisielowski)
Non-corrected HREM
Au
Cs-corrected HREM
HREM approaches the physical limits by interaction processThus the same limits as electron diffraction